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EP1062604A1 - Procede et dispositif pour determiner une defaillance d'un systeme technique - Google Patents

Procede et dispositif pour determiner une defaillance d'un systeme technique

Info

Publication number
EP1062604A1
EP1062604A1 EP99911580A EP99911580A EP1062604A1 EP 1062604 A1 EP1062604 A1 EP 1062604A1 EP 99911580 A EP99911580 A EP 99911580A EP 99911580 A EP99911580 A EP 99911580A EP 1062604 A1 EP1062604 A1 EP 1062604A1
Authority
EP
European Patent Office
Prior art keywords
value
support point
approximation process
determined
matrix
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
EP99911580A
Other languages
German (de)
English (en)
Other versions
EP1062604B1 (fr
Inventor
Georg Denk
Oliver Schein
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Siemens AG
Siemens Corp
Original Assignee
Siemens AG
Siemens Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Siemens AG, Siemens Corp filed Critical Siemens AG
Publication of EP1062604A1 publication Critical patent/EP1062604A1/fr
Application granted granted Critical
Publication of EP1062604B1 publication Critical patent/EP1062604B1/fr
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Definitions

  • the differential-algebraic system of equations (1) is also called the quasilinear-implicit system of equations.
  • X (t) denotes a curve of node voltages that is dependent on a time t
  • x (t) is its derivative after the time t.
  • F (x (t)) denotes a first predetermined function which contains guide values and non-linear elements
  • c (x (t)) a predetermined capacitance matrix
  • s (t) a second predetermined function, which are independent voltage sources and Contains power sources.
  • Equation (1) only describes the ideal case for a circuit. In practice, however, noise, i.e. a malfunction of the circuit, do not avoid. Noise is an unwanted signal disturbance caused, for example, by thermal effects or the discrete structure of the elementary charge. Due to the increasing integration density of integrated circuits, the importance of predictive analysis of such effects (noise simulation) is growing.
  • equation (1) When analyzing a circuit considering noise, equation (1) can be modeled as:
  • v ( ⁇ , t) denotes an m-dimensional vector whose independent components are generalized white noise, where m indicates the number of interference current sources.
  • a matrix ⁇ (t, x (t)), also referred to as an intensity matrix, has the dimension n x m. If only thermal noise occurs in linear resistors, it is constant.
  • index is to be understood in the following as a measure of how far a differential-algebraic system of equations “differs” from an explicit ordinary differential equation system, how many derivation steps are required to obtain an explicit ordinary differential equation system from the differential-algebraic system of equations .
  • index a differential-algebraic system of equations:
  • the disturbance is decoupled into a differential and an algebraic part.
  • the intensity matrix depends only on the time t.
  • a tuft of matrix ⁇ C + G; ⁇ s C ⁇ is regular if a ⁇ g from C exists such that:
  • the aim of the transformation is to convert regulation (11) into a semi-explicit system of differential equations of the type
  • a matrix C is a right upper triangular matrix whose r first diagonal elements are not equal to zero.
  • the matrix C has from the (r + l) th row including only entries with the value zero.
  • the matrix Q] _ is chosen as the orthogonal column permutation matrix.
  • the matrix l is the product of a lower left triangular matrix and an orthogonal row permutation matrix.
  • y is converted into a first vector y * -, which contains the first r components, and into a second vector yfe L i ' , which contains the rest
  • the matrix E is a unit matrix of dimension rxr and the matrices E 2 , E3 and E4 are zero matrices. Thus (25) is divided into the two regulations (14) and (15). 9 If the matrix F4 is invertible, which is exactly the case if the system has the index 1 from regulation (12), then regulation (15),
  • F: F ⁇ - F 2 • F 4 _1 • F 3 ; (29)
  • dY yW -
  • * is a random variable with an expected value to y t (to) that has a finite variance.
  • ⁇ Wt; te 9? Q > is a Wiener-Hopf process of the dimension of the number of sources of noise, generally the number of sources of interference.
  • the expected values E ⁇ and the second moments are approximately determined in the method from [2] by numerical integration with linear implicit multi-step methods.
  • a disadvantage of this method is that in order to determine the second moments P ⁇ - linear systems of equations of quadratic order in the number m of noise sources are solved for each time step.
  • the method is based on a manual index reduction of the differential algebraic system of equations to an explicit stochastic system of differential equations, which cannot be automated. In addition, only some of the noise effects are considered. Furthermore, the method does not provide path-wise 12 se information, but only the moments of the node potentials that are retained when the index is reduced. This method does not provide any information for the node potentials that are suppressed by the index reduction.
  • [5] describes a circuit description language SPICE with which an electrical circuit can be written in a form that can be processed by a computer.
  • an output unit 13 includes.
  • the initialization unit supplies the initialization value of a state and a function with which a system which is subject to a random fault is described to the incrementing unit.
  • the incrementing unit uses two sequences of random numbers to form an increment of the estimated value without differentiating the function itself. In the unit for updating an estimated value, the estimated value is increased by the increment.
  • [8] also discloses a method and a device for improving the accuracy of a system controlled in a closed control loop, at least two stochastic interference signals being taken into account.
  • the invention is therefore based on the problem of specifying a method with which the disadvantages described above are avoided.
  • T is a predetermined value, which is divided into N subintervals
  • - G is a second matrix
  • the device according to claim 12 has a processor unit which is set up in such a way that a technical system which is subject to a fault is described by means of an implicit stochastic differential equation system.
  • An approximate solution to the system is determined by implementing a discrete approximation process.
  • the discrete approximation process is implemented according to the following regulation: 15
  • T - h: -, a step size in an initial time interval N -
  • T is a predetermined value, which is in N
  • a difference value ⁇ W n _ ⁇ : W ⁇ - W ⁇ - between a second value W ⁇ at the support point ⁇ n and the second value W t n -1 at the support point ⁇ n _ ⁇
  • the invention directly uses the implicit structure of the technical system represented by an implicit system of differential equations.
  • the determination of the fault is considerably accelerated by the invention since the thin occupation of the matrices C and G can be used.
  • the 16 numerically unstable and complex transformation of the system of differential equations into the decoupled form is omitted.
  • the invention makes it possible for the first time to determine a fault even with a singular matrix C.
  • the invention can be used in a wide variety of fields of application in which a technical system is disturbed and can be described by a system of differential algebraic equations.
  • interference can be determined in an electrical circuit.
  • the invention is also suitable for use in a mechanical multibody system or in a general physical system, a chemical system or also a physico-chemical system, the respective modeling of which leads to a system of differential algebraic equations.
  • FIG. 1 is a flowchart showing the individual process steps
  • Figure 2 shows an apparatus with which the method is carried out
  • Figure 3 is a sketch of an electrical circuit of a differentiator
  • FIG. 4 shows a simulation result. 17
  • FIG. 2 shows a computer R in the form of a block sketch, with which the method described below is carried out.
  • the computer R has a processor unit P which is set up in such a way that the method steps described below can be carried out.
  • the processor unit P is connected via a bus B to a memory SP.
  • the computer R is connected via a first interface I / O 1 to a keyboard TA and via a second interface I / O 2 to a mouse MA, with which a user of the computer R can make inputs.
  • the computer R is connected to a screen BS on which the results of the method are presented to the user.
  • the circuit S to be analyzed is in the memory SP
  • circuit description language (see FIG. 3) stored in the form of a circuit description language.
  • the network list format from SPICE is used as the circuit description language.
  • FIG. 1 An equivalent circuit diagram of the circuit S for this exemplary embodiment is shown in FIG.
  • the functionality of the circuit S represents a differentiator.
  • An independent voltage source V (t) is arranged between a first node N ] _ and a ground potential NQ.
  • a capacitance C Q is provided between the first node and a second node N 2 .
  • the second node N is connected via a resistor R to a third node N3.
  • a noise current source RS with the current strength ⁇ l R is connected in parallel with the resistor R.
  • a first input E1 of an operational amplifier OV is connected to the second node N 2
  • An output A of the operational amplifier OV is connected to the third node N3.
  • the circuit S is stored in a first step 101 in the form of the SPICE network list format in the memory SP (cf. FIG. 1).
  • a modified node analysis is carried out for the circuit S.
  • the result of the modified node analysis is the system of equations belonging to the circuit S.
  • A denotes a gain factor of the operational amplifier OV.
  • v ( ⁇ , t) describes as white noise the driving generalized stochastic process, i.e. the disturbance of the technical system.
  • the quantities k, T and ⁇ f are given as constants.
  • the rule (42) is the stochastic system of differential equations of the form
  • a numerical method provides for every natural number N realizations of a discrete approximation process
  • x s ; s XQ, ..., ⁇ n
  • a function without arguments stands for an evaluation at the point l ⁇ n , X ⁇ ).
  • the real parameters ⁇ _k, ⁇ 2 , and ⁇ k are selected from the interval [0, 1].
  • the size V n is also given by 21
  • ⁇ n : W Tn + 1 - W Tn (46)
  • the size b beeschhrhr gives the multiple It ⁇ - bl> 32 ⁇ ⁇ n ' ' ⁇ n + l
  • regulation (53) specifies a regulation with which the malfunction of the system can be determined. Regulation (53) can also be applied in the case of index 1.
  • the disturbance X N n + 1 is determined by iteratively solving the approximation process.
  • a circuit S is modified so that the specifiable conditions e.g. with regard to the susceptibility of the circuit S to failure.
  • the modified circuit is fired in silicon in a final step.
  • FIG. 4 shows the result of the method carried out by the computer R, which is indicated below as a program.
  • a numerically simulated solution path RLP of the voltage curve in the third node N3 is shown, taking into account the noise.
  • the ideal solution path ILP ie the solution path without taking into account the noise, is given for comparison.
  • the course V of the input variable V (t) is also shown. 24 The following parameters were used for the procedure:
  • the capacity matrix can also be singular without further ado. This makes it possible for the first time to take a singular capacity matrix into account.
  • the invention is in no way limited to the determination of thermal noise.
  • any model of a disturbance which can be described or approximated by white noise, e.g. the shot noise in power sources.
  • the current source is modeled by a randomly connected current source connected in parallel, the current strength ⁇ IQ of the regulation
  • ⁇ IQ ⁇ 2eIciet ⁇ f ' v ( ⁇ ' t)
  • the implementation of the noise simulation method is also given in the FORTRAN77 programming language.
  • C n is the dimension of the system, m is the number of C noise sources
  • C num is the number of subintervals under consideration
  • C i and j are auxiliary variables for loops
  • C info asks the return code
  • C initl and init2 are the seeds for the C pseudo random number generator C.
  • DOUBLE PRECISION C (n, n), G (n, n), B (n, m), A (n, n)
  • C xakt describes the value of the solution process at time C tauakt
  • C C, B and G are the matrices of the problem of regulation C (3)
  • C A and d are used to build the equation C salt and sakt describe s (taukt) and s (takt - 1)
  • C h * _ * denote auxiliary vectors and matrices
  • C outer loop corresponds to the treatment of a C subinterval

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Microelectronics & Electronic Packaging (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Design And Manufacture Of Integrated Circuits (AREA)

Abstract

Selon l'invention, on décrit un système technique subissant une défaillance, au moyen d'un système d'équations différentielles stochastique implicite. On détermine une solution approximative du système au moyen d'un processus d'approximations discrètes selon la règle (a). La défaillance (b) est déterminée par solution itérative du processus d'approximation.
EP99911580A 1998-03-18 1999-01-29 Procede et dispositif pour determiner une defaillance d'un systeme technique Expired - Lifetime EP1062604B1 (fr)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
DE19811860 1998-03-18
DE19811860 1998-03-18
PCT/DE1999/000239 WO1999048030A1 (fr) 1998-03-18 1999-01-29 Procede et dispositif pour determiner une defaillance d'un systeme technique

Publications (2)

Publication Number Publication Date
EP1062604A1 true EP1062604A1 (fr) 2000-12-27
EP1062604B1 EP1062604B1 (fr) 2001-11-07

Family

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EP99911580A Expired - Lifetime EP1062604B1 (fr) 1998-03-18 1999-01-29 Procede et dispositif pour determiner une defaillance d'un systeme technique

Country Status (4)

Country Link
US (1) US6556954B1 (fr)
EP (1) EP1062604B1 (fr)
DE (1) DE59900409D1 (fr)
WO (1) WO1999048030A1 (fr)

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US7268924B2 (en) * 2001-01-22 2007-09-11 Hand Held Products, Inc. Optical reader having reduced parameter determination delay
US20020141347A1 (en) * 2001-03-30 2002-10-03 Harp Jeffrey C. System and method of reducing ingress noise
DE10126018A1 (de) 2001-05-28 2003-02-27 Infineon Technologies Ag Verfahren zum Bereitstellen von Fehlerinformationen über Inkonsistenzen in einem System von Differentialgleichungen
DE10154200C1 (de) * 2001-11-07 2003-03-06 Infineon Technologies Ag Verfahren zum Erzeugen wenigstens einer Folge von an Zahlenfolgen eines 1/f-Rauschens angenäherten Zufallszahlen
US7415395B2 (en) * 2001-12-21 2008-08-19 Caterpillar Inc. Symbolic evaluation engine for high-performance simulations
EP1343061A1 (fr) * 2002-03-08 2003-09-10 Siemens Aktiengesellschaft Procédé de simulation d 'un système technique et simulateur
US6992524B2 (en) 2003-09-08 2006-01-31 Skyworks Solutions, Inc. Quiescent current control circuit for high-power amplifiers
DE102005013286B3 (de) * 2005-03-22 2006-09-14 Siemens Ag Verfahren zur Erfassung von Fehlerursachen und deren transiente Auswirkungen auf ein technisches System
US20070162505A1 (en) * 2006-01-10 2007-07-12 International Business Machines Corporation Method for using psychological states to index databases
US7650271B2 (en) * 2006-03-31 2010-01-19 Intel Corporation Time-domain device noise simulator
US8726203B1 (en) 2013-04-25 2014-05-13 Cydesign, Inc. System and method for generating virtual test benches
US10448938B2 (en) 2016-06-16 2019-10-22 Phillips Medical, LLC Methods and systems for sealing a puncture of a vessel

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DE3933471A1 (de) 1989-10-06 1991-04-18 Schenck Ag Carl Verfahren und vorrichtung zur verbesserung der dosiergenauigkeit einer geregelten differentialdosierwaage
JP3735128B2 (ja) 1993-11-10 2006-01-18 富士通株式会社 シミュレーション装置
US5537329A (en) * 1994-06-30 1996-07-16 At&T Corp. Apparatus and method for analyzing circuits
US6182270B1 (en) * 1996-12-04 2001-01-30 Lucent Technologies Inc. Low-displacement rank preconditioners for simplified non-linear analysis of circuits and other devices
US6072947A (en) * 1997-09-23 2000-06-06 Lucent Technologies, Inc. Method of making an integrated circuit including noise modeling and prediction
US6135649A (en) * 1998-03-09 2000-10-24 Lucent Technologies Inc. Method of modeling and analyzing electronic noise using Pade approximation-based model-reduction techniques
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Also Published As

Publication number Publication date
DE59900409D1 (de) 2001-12-13
EP1062604B1 (fr) 2001-11-07
WO1999048030A1 (fr) 1999-09-23
US6556954B1 (en) 2003-04-29

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